Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(n,k) = n! * Sum_{j=0..n} j^k/j!.

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =1a(5) =5a(6) =0a(7) =1a(8) =4a(9) =16a(10) =0a(11) =1a(12) =6a(13) =15a(14) =65a(15) =0a(16) =1a(17) =10a(18) =27a(19) =64a(20) =326a(21) =0a(22) =1a(23) =18a(24) =57a(25) =124a(26) =325a(27) =1957a(28) =0a(29) =1